{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Решение задачи Коши для ОДУ\n",
    "Задача Коши – это задача для обыкновенного дифференциального уравнения (ОДУ), в которой известны начальные условия. Для решения задачи Коши вы можете использовать библиотеку scipy в Python. Вот пример решения задачи Коши для простого ОДУ\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Определяем дифференциальное уравнение\n",
    "def ode(x, y):\n",
    "    dydx = -2 * y\n",
    "    return dydx\n",
    "\n",
    "# Начальные условия\n",
    "x0 = 0.0  # Начальная точка\n",
    "y0 = 1.0  # Начальное значение y(0)\n",
    "\n",
    "# Интервал интеграции\n",
    "x_span = (0.0, 5.0)  # От 0 до 5\n",
    "\n",
    "# Решение задачи Коши\n",
    "sol = solve_ivp(ode, x_span, [y0], t_eval=np.linspace(x_span[0], x_span[1], 100))\n",
    "\n",
    "# Извлечение результатов\n",
    "x_values = sol.t\n",
    "y_values = sol.y[0]\n",
    "\n",
    "# Построение графика решения\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_values, y_values, label='Решение', color='blue')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y(x)')\n",
    "plt.title('Решение задачи Коши для ОДУ')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LJscvAcCzzz57z/3c78/ozTffRJcuXfDYY49VOLbxXgdZXL16Ffn5+YavZktr1qwZdDodzp8/jxYtWtzjVQBnz54FgAr3tXnzZuTl5cHT07PS/Vy7dg3Ozs5mzTLyzTff4K+//sJ3332H1atXG913/vx5uLi43PMrSZVKhaCgIMO4Nf21/p/HytSrV8+w/alTpwCIX61W5NatW6hVq5bhdtnPTqNGjaBWqw3jGK3xGTNHRkYGPv30UyxZssTkH7Rz585h2rRp+Pnnn8uNo79165bRbXM+e59//jk+//xzAOKYy8jISCxYsMBw4K6elM/d2bNnTQ410Ae9s2fPmhxjWpYlPkOjRo1CXFwczp49iwYNGmDdunXQarV45plnym1b9j2gUqnQuHFjozGv5rT/+fPnjd4rgYGB+P7778v9PLZs2XLP95Tcfwvq1KmDJk2a4LPPPkPXrl0RFhYGtVqNwsJCs54DEL++f/vtt/Hcc8/h5ZdfNrpPP8xBr0aNGkb/ZFTEUr8jpTD3/S3lfdWhQwf8+uuvmD59Op599ll4eHiUez/p6f/JrFGjhqR633rrLezZswcqlarCf3pWrlyJ999/HydOnIBWqzWsLzt8xJoYeK2offv25X7Zl6bT6RAdHY033njD5P0PPvhglWvQ6XRQqVT43//+B41GU+7+sr84Q0JCyo07XbduXYVj9q5du4Z58+YhISHB6L/i0s/v5+dn1ENSmpRfqPpfYAEBAffcFhAPYFixYgVWrVpV6fjgadOmoUuXLkbrHn/8caPb9/Mz2rJlC7Zu3Yq0tLRK69T/Q6SXk5ODJ554otLHyC0zMxP169eXPAVQUVERpk6diueee85kW5k7h6b+wJ77fZy+53HevHkVjiu7V7gr+9qr+zNmrrfeegtNmjTB6NGjyx3gVFJSgujoaPz777+YPHkymjZtCk9PT1y8eBFjxowp1zNrzmdvwIABiIuLgyAIyMjIwMyZM/HYY4/h1KlTRr1TUj53SjJ8+HC89tpr+OabbzBlyhSsWrUKERERJoPRvZjb/v7+/li1ahUAMQx/8cUX6N27N3bu3IlWrVoZtouMjMTs2bONHvvxxx/jp59+MtyW+28BIAbVkSNHIiYmxmi9OSEyOTkZo0aNQr9+/bB06dJy95edBvLLL78sd8CYPXrttddw8uRJzJo1CzNmzKh0W31Qlnrcxt69e7FixQp8/PHHeOGFF5Cenm70rc+qVaswZswYDBw4EJMmTYKfnx80Gg2SkpLKHWxsTQy8CtKoUSPk5uZW63QqjRo1giAICA0NlRSgPT09y9WTnp5e4fazZ8+Gt7c3JkyYUOHzb926FZ06dZL0X7Yp+q93yn6NV5GEhASEhYVh2LBhlW7XqlWrcq+17B8Cc39GgiDgzTffxKBBg/DII49Uum3Zf4jKfrVbt25deHh44OTJk+Uee+LECajVagQHB0uqq0GDBgBQ4b58fX3v+UenuLgYhw8fRu/evSU9JwB88sknuHLlSoUngwgMDERRURGuX79e6VedgiDg8uXLhiO19X/ULl26dM95ji9evIigoCAAMHwV5+PjI/lneurUKaNeitOnT0On0xn+WFT3Z8wchw4dwpo1a7BhwwaToebPP//E33//jZUrVxoOVgHEEGGKOZ+9Bx54wOh1eXl5YeTIkTh06BAeffRRw3opn7sGDRpU+F7V3y+FJT5DtWvXRr9+/fDNN99g5MiR2LVrV4UHq+q/QdATBAGnT59G69atAZjf/m5ubkZt1b9/f9SuXRsff/wxPv30U8N6X1/fcm26YcMGo9ty/y0AgLZt22L58uXo0qULZs6ciUceeQTz5s0rN0NKRfbu3YtBgwYhIiIC3333HZycykeasm0p5RswwDK/I6Uy9/19r/cVIA6VWb58OQ4dOoQaNWogMTERhw8fxuuvv17uefQz11TWIVfajBkzMHr0aISFhSEiIgKzZ8/GrFmzDPevX78eDRs2xA8//GDUIZCYmChp/9WFY3gVZOjQoUhLS8PmzZvL3Xfz5k0UFxdX+TkGDx4MjUaDGTNmQBAEo/sEQcD169fve9+ZmZlYsmQJpk+fXmGYHTp0KEpKSow+HHrFxcWGr0wrs3btWpPj1kxJS0vDTz/9hPfee88iE5Gb+zNas2YNjhw5UuXZIQAxBPTq1Qs//fST0VdX2dnZWL16NTp37gwfHx9J+woMDERYWBhWrlxp1OZHjx7Fli1b0Ldv33vuY8uWLbh165bJaZpMuX37Nt555x289tprFfYQ6oPQjz/+aFi3d+9eAMC+ffsM61JSUnD79m3D9pU9bv/+/YZ1f//9N44dO2bYPjw8HI0aNcL8+fPLTd0HiF+Bl7V48WKj2x999BEAcZ5toHo/Y+Z688030alTJ/Tv39/k/fpgWbpOQRCwaNEik9ub89krS99baSp430vfvn2xb98+o29J8vLysGzZMoSEhKB58+aS9mOpz9AzzzyDY8eOYdKkSdBoNBg+fLjJ7b766ivcvn3bcHv9+vW4fPmy4b1ibvuXVVRUhOLi4vsaBiD33wJA/BbrmWeeQf/+/fH2228jKipK8ol5jh8/jn79+iEkJAS//vprhc8TFRVldJG6f0v8jpTK3Pf3vd5XegkJCTh37hxWrVqFqKgohIeHm3z+9evX46GHHkLTpk0l1av/RqZNmzZ4/fXXMWfOHBw9etRwv6n39d69e+/5LWd1Yw+vgkyaNAk///wzHnvsMYwZMwbh4eHIy8vDn3/+ifXr1yMzM9NobOPJkyexadMmw+3c3Fyo1Wqjdf/884/RczRq1AizZ89GQkICMjMzMXDgQHh7eyMjIwM//vgjXnjhBZP/AUqxfft2NGvWDLGxsRVu07VrV7z44otISkpCeno6evXqBWdnZ5w6dQrr1q3DokWL8OSTT5p87B9//IGpU6di06ZNWLp0qaQAu2XLFkRHR1us19zcn9GWLVswduzY+/q605TZs2cjOTkZnTt3xrhx4+Dk5IRPP/0UhYWFmDt3rln7mjdvHvr06YMOHTrgueeeM0y5U6NGjXuejnft2rV4/fXX4erqijt37hi+ZgXEr1pLSkqwYcMGDBw40LD+4MGD8PX1rXA4CAB0794dHTp0wCuvvIKzZ89Co9Hgs88+AwB8//33hh64uXPnIjQ01BA0GjZsiOHDhyMpKQm5ubmoV6+e4avWP/74A8OHD0dkZCQWLVqEGjVqGMb5qdVqfPbZZ+jTpw9atGiB2NhY1KtXDxcvXsS2bdvg4+ODX375xajGjIwM9O/fH71790ZaWhpWrVqFp556Cm3atAFQvZ+xq1evGn2+AXEMKABs2rQJ7du3N/r6eMuWLZX2ljVt2hSNGjXC66+/josXL8LHxwfff/99ubGk9/PZO3fuHDZt2mQY0vDOO++gQYMGaNu2rTkvGYAY3L/99lv06dMHr776KmrXro2VK1ciIyPD8L6QyhKfoX79+qFOnTpYt24d+vTpU+ExCbVr10bnzp0RGxuL7OxsLFy4EI0bN8bYsWMBSG9/vby8PKMhDV9//TUKCgrKTVslhdx/CwDxANA7d+4YPuNS3b59GzExMbhx4wYmTZpUbr7aRo0aoUOHDmbXXVZVfkeaw9z3973eV4A4pdoHH3yAr7/+usJvQP755x/MnTsX+/btw+DBg41+j+s7CpKTk1G/fn2jgzxLS0xMxPfff4+xY8di165dUKvVeOyxx/DDDz9g0KBB6NevHzIyMrB06VI0b97cZMeC1VhrOghHJmX6E73bt28LCQkJQuPGjQUXFxfB19dX6NixozB//nyhqKhIEIS7U16Zc9FPS6b3/fffC507dxY8PT0FT09PoWnTpsL48eOFkydPGrYxdyoalJomSs/UVDqCIE6nEx4eLri7uwve3t5Cq1athDfeeEO4dOlShW0zZ84coV27dianLqtoaiSVSiUcOHDAaNuyU2SZM32MIJj3M3J3dxcuXrxo9Piy0/aYMy2ZIIhTd8XExAheXl6Ch4eH0L17d2H37t0m2+Ne77mtW7cKnTp1Etzd3QUfHx/h8ccfF44dO1bpY/Sv4V7vudI/965duwoADNOB6ZWdPksQxCnG+vXrJ7i5uQnt2rUzTI+zaNEi4bHHHhPc3NyERx55RDhx4oTR427fvi08/fTTgoeHh9C0aVPD1GVTpkwRxowZI7i7uwstW7Ys11aCIAiHDh0SBg8eLNSpU0dwdXUVGjRoIAwdOlRISUkpV+uxY8eEJ598UvD29hZq1aolxMXFGU39o1ddn7HKLvophPS1DhgwwGi/pacV0jt27JgQFRUleHl5Cb6+vsLYsWOFw4cPG02rdz+fPf1FpVIJAQEBwuDBg4Xjx4+Xq0Xq5+7MmTPCk08+KdSsWVNwc3MT2rdvL/z6668mX19l05IJgrTP0L3op6NbvXp1ufv0dXz77bdCQkKC4OfnJ7i7uwv9+vUrN9WblPYXBPF3ael29fLyEh5++GHh66+/NtqfOdPXCYJ8fwu+/fZbQaVSCZs2bSq33b2mJbvX38Cy7x1Tqvt3ZHW+v+/1vrp27ZoQFBQkjBgxotKa9G1wr4v+fWjq94cgCEJqaqqgUqkM06LpdDrh3XffFRo0aCC4uroKbdu2FX799dcK84C1MPASkdkaNGhg9Me4rG3btlnsF9v+/fvL/fGXoqJ/GO6XPkRevXrVIvuzNFN/iKj6TJw4UfD29hby8vLK3Sc1eBOZw9Lvqy+//PKev6e7du1q9u9epeIYXiIiIjMUFBRg1apVeOKJJ8yako+I5MMxvERktkGDBpWbbLw0f3//+xpXSPcvJiamwumfyDKuXLmCrVu3Yv369bh+/XqlMxAQKV2jRo3u+Xs6Ojq60t/1toSBl4jM9sEHH1R6f7Nmze65DVlW2YPZyPKOHTuGkSNHws/PDx9++GGFczcT2YIuXbqUmwO7rLfeestK1VQ/lSCUmY+EiIiIiMiOcAwvEREREdk1Bl4iIiIismscw2uCTqfDpUuX4O3tbZGzcxERERGRZQmCgNu3byMoKOieJ6Bh4DXh0qVL9zyfOhERERHJ7/z583jggQcq3YaB1wRvb28AYgNKOa96VWm1WmzZssVwml2qGNvKPGwv6dhW0rGtpGNbSce2ko5tJcrJyUFwcLAht1WGgdcE/TAGHx8fqwVeDw8P+Pj4OPQbVwq2lXnYXtKxraRjW0nHtpKObSUd28qYlOGnPGiNiIiIiOwaAy8RERER2TUGXiIiIiKyaxzDS0RERHZJEAQUFxejpKRE7lIsSqvVwsnJCQUFBXb32krTaDRwcnKyyBSxDLxERERkd4qKinD58mXk5+fLXYrFCYKAgIAAnD9/3u7PF+Dh4YHAwEC4uLhUaT8MvERERGRXdDodMjIyoNFoEBQUBBcXF7sKhjqdDrm5ufDy8rrnCRdslSAIKCoqwtWrV5GRkYEmTZpU6bUy8BIREZFdKSoqgk6nQ3BwMDw8POQux+J0Oh2Kiorg5uZmt4EXANzd3eHs7IyzZ88aXu/9st9WIiIiIodmz2HQUVjqZ8h3AhERERHZNQZeIiIiIrJrDLxEREREZNcYeImIiIgUYsyYMVCpVFCpVHBxcUHjxo0xc+ZMFBcXy12aTeMsDUREREQK0rt3b3z55ZcoLCzExo0bMX78eDg7OyMhIUHu0mwWe3iJiIjI7gkCkJcnz0UQzKvV1dUVAQEBaNCgAV5++WVERUXh559/BgDs3LkTXbt2RWBgIBo0aIBXX30VeXl5hseGhIRg4cKFhtsLFy5ESEiI0f5VKhU2bNhguH3+/HkMHToUNWvWRO3atTFgwABkZmYa7h8zZgwGDhxotI8VK1agZs2ahtvTp09HWFiY4XZRUREaN24MlUqFmzdvGtbv3LkTXbp0gbu7O4KDg8vVX10YeImIiMju5ecDXl7yXKp6sjd3d3cUFRXhzJkz6N27NwYPHoydO3fi22+/xc6dOxEXF3ff+9ZqtYiJiYG3tzd27NiBXbt2wcvLC71790ZRUdF97/fjjz9Gdna20Tp9/U888QSOHDmCtWvXVrl+qRh4iYiIiBRIEARs3boVmzdvRo8ePZCUlISRI0diwoQJaNSoETp27IgPP/wQX331FQoKCu7rOdauXQudTofPPvsMrVq1QrNmzfDll1/i3LlzSE1Nva99/vvvv5g9ezYmT55stF5f/8SJE9GkSROL1C8Vx/BSpW7eBP78E6hTB2jeXO5qiIiI7o+HB5CbK99zm+PXX3+Fl5cXtFotdDodnnrqKUyfPh3dunXDkSNH8M033xi2FQTBcCrlZs2amV3b4cOHcfr0aXh7exutLygowJkzZ8rVpFdcXFzhmc9mzpyJ7t27o3PnzuWey9L1S8XASwZ5ecAvvwCHD4sh98gR4Px58T4nJ2D7dqBjR3lrJCIiuh8qFeDpKXcV0nTv3h1LliyBi4sLgoKC4OQkxrXc3Fy8+OKLiIuLQ25uLry8vAxnIqtfv/59PVdubi7Cw8ONQqhe3bp1y9Wk98MPP+Ddd98t95hTp07hs88+Q3p6Oi5cuFDuuV588UW8+uqr5R53v/VLxcBLBs89B6xdW369jw+QkwMMGwYcOgT4+lq/NiIiIkfh6emJxo0bl1v/8MMP49ixY2jcuDFycnLg4+NT5VPvPvzww1i7di38/Pzg4+MjuSY/Pz+T202ePBnPP/88GjduXC7wlq7f2jiGlwAA//wDrFsnLo8dCyxeDOzYAdy4AVy4ADz4oHj99NOATidvrURERI5o8uTJ2L17N1555RX8+eefOHXqFH766adyB30VFxejoKAABQUFKC4uhiAIhttlx8qOHDkSvr6+GDBgAHbs2IGMjAykpqbi1VdfLRdY7+X06dNITU3FtGnTKq0/Li4O6enpFdZfHdjDSwCARYvEIBsTAyxbVv7+9euByEhg82bgnXeAqVOtXyMREZEja926NbZv344pU6agb9++EAQBjRo1wrBhw4y2mzRpEiZNmmS0zt3d3eQ+PTw88Pvvv2Py5MkYPHgwbt++jXr16qFnz56V9viakpeXhxkzZqB27dqV1v/WW2+hS5cuFdZfHRh4CTduAJ9/Li7/5z+mt2nVCvjkEyA2FkhMFMfy9uxpvRqJiIgcwYoVKyq9v127dti8eXOFQxpKz58rVUBAAFauXGlWTWPGjMGYMWMMt6dPn47p06cbbdOtWzcIZSYhbteuHbZs2WJ2jVXFIQ2EZcvEA9ZatQKioirebswY4NlnxQm0n3oKuHTJaiUSERER3TcGXgdXVAR8+KG4HB8vHsVamY8/Blq3Bq5cAUaMAHhqbyIiIlI6Bl4Ht3at2FMbECAG2HtxdxfH83p7A7//DsyYUf01EhEREVUFA68DEwRgwQJx+ZVXAFdXaY9r0gRYvlxc/uAD4Nat6qmPiIiIyBIYeB3Ytm1Aerp4BpiXXjLvsUOHimdey8sDvvqqWsojIiKqkrIHTJHtsdTPkIHXgb3/vngdGwtUMINIhVQqYNw4cfmTT8TeYiIiIiVwdnYGAOTn58tcCVWV/meo/5neL05L5qCOHwc2bhSD68SJ97ePZ54B3nwTOHEC+O03TlNGRETKoNFoULNmTVy5cgWAONes6l5HZdsQnU6HoqIiFBQUVPlMa0olCALy8/Nx5coV1KxZExqNpkr7Y+B1UPqxuwMGAPd7hj8fH2DUKLGHd/FiBl4iIlKOgIAAADCEXnsiCALu3LkDd3d3uwryptSsWdPws6wKBl4HdOUK8PXX4nJFJ5qQatw4MfD+9JN46uEHHqh6fURERFWlUqkQGBgIPz8/aLVaucuxKK1Wi99//x2PPvpolb/qVzJnZ+cq9+zqMfA6oB9/BAoLgYgIoFOnqu2rRQugWzcgNRX49FNg1ixLVEhERGQZGo3GYqFJKTQaDYqLi+Hm5mbXgdeS7HPgB1Xqjz/E6+joe59oQgr9wWvLl4snsiAiIiJSEgZeB6QPvBERltnfwIFAUBCQnQ18/71l9klERERkKYoIvIsXL0ZISAjc3NwQGRmJffv2VbjtDz/8gIiICNSsWROenp4ICwvD1/oBqf9vzJgxUKlURpfevXtX98uwCQUFwNGj4rKlAq+zM/DCC+Ly4sWW2ScRERGRpcgeeNeuXYv4+HgkJibi4MGDaNOmDWJiYio8qrJ27dp46623kJaWhiNHjiA2NhaxsbHYvHmz0Xa9e/fG5cuXDZdvv/3WGi9H8Y4cAYqLgbp1geBgy+137FjAyQnYtQs4fNhy+yUiIiKqKtkPWluwYAHGjh2L2NhYAMDSpUvx3//+F1988QXefPPNctt369bN6PaECROwcuVK7Ny5EzExMYb1rq6ukqexKCwsRGFhoeF2Tk4OAPEoSGsc2al/Dms81969agAahIfrUFxcYrH91q0LDBigwfffq/HxxyX45BOdxfZdmjXbyh6wvaRjW0nHtpKObSUd20o6tpXInNevEmQ8715RURE8PDywfv16DBw40LB+9OjRuHnzJn766adKHy8IAn777Tf0798fGzZsQHR0NABxSMOGDRvg4uKCWrVqoUePHpg9ezbq1Kljcj/Tp0/HjBkzyq1fvXo1PDw87v8FKtBHH4UhJaUBhgw5iZEjT1h030eP1sHbb3eGq2sxPv98M7y8ii26fyIiIiK9/Px8PPXUU7h16xZ8fHwq3VbWwHvp0iXUq1cPu3fvRocOHQzr33jjDWzfvh179+41+bhbt26hXr16KCwshEajwSeffIJnn33WcP+aNWvg4eGB0NBQnDlzBlOmTIGXlxfS0tJMTk1iqoc3ODgY165du2cDWoJWq0VycjKio6OrfXqRhx92wtGjKqxfX4z+/S37oxcEoG1bJxw7psLChSUYN87yvbzWbCt7wPaSjm0lHdtKOraVdGwr6dhWopycHPj6+koKvLIPabgf3t7eSE9PR25uLlJSUhAfH4+GDRsahjsMHz7csG2rVq3QunVrNGrUCKmpqehp4nRgrq6ucHV1Lbfe2dnZqm+k6n6+/HzxlMIA8MgjTqiOp3r+eSA+HtiwQYMJE6pv3kNr/2xsHdtLOraVdGwr6dhW0rGtpHP0tjLntct60Jqvry80Gg2ys7ON1mdnZ1c6/latVqNx48YICwvDf/7zHzz55JNISkqqcPuGDRvC19cXp0+ftljttujwYaCkBAgIEKcRqw6DBonXv/8OXLtWPc9BREREZA5ZA6+LiwvCw8ORkpJiWKfT6ZCSkmI0xOFedDqd0ZCEsi5cuIDr168jMDCwSvXaOv38u+HhljnhhCkhIUBYGKDTAb/8Uj3PQURERGQO2acli4+Px/Lly7Fy5UocP34cL7/8MvLy8gyzNowaNQoJCQmG7ZOSkpCcnIx//vkHx48fx/vvv4+vv/4aTz/9NAAgNzcXkyZNwp49e5CZmYmUlBQMGDAAjRs3NprFwRFZ+oQTFdH38v74Y/U+DxEREZEUso/hHTZsGK5evYpp06YhKysLYWFh2LRpE/z9/QEA586dg1p9N5fn5eVh3LhxuHDhAtzd3dG0aVOsWrUKw4YNAyCeX/rIkSNYuXIlbt68iaCgIPTq1QuzZs0yOU7XkRw4IF5bI/AmJgJbtgC5uYCXV/U+HxEREVFlZA+8ABAXF4e4uDiT96Wmphrdnj17NmbPnl3hvtzd3cudhILE4Kk/YC08vHqfq2VLoFEj4MwZYNMm4Mknq/f5iIiIiCoj+5AGso70dHFcbVAQUN1DmVUqDmsgIiIi5WDgdRDWGr+rpw+8//0vUFRkneckIiIiMoWB10FYa/yu3iOPiNOf3boFlBmVQkRERGRVDLwOwto9vGo1MGCAuMxhDURERCQnBl4HkJMDnDwpLlf3AWul6Yc1/PSTOH6YiIiISA4MvA7g0CFAEIDgYMDPz3rP27074OMDXL4M7N1rveclIiIiKo2B1wFYeziDnosL0K+fuMxhDURERCQXBl4HYO0D1korPT2ZIFj/+YmIiIgYeB2AXD28ANCnD+DqCpw+Dfz1l/Wfn4iIiIiB187dvAmcOiUuW/OANT0vLyA6WlzmsAYiIiKSAwOvnTt4ULwOCQHq1JGnBp51jYiIiOTEwGvn5By/q/f44+K8vIcOAWfPylcHEREROSYGXjsn5/hdvbp1gY4dxeUtW+Srg4iIiBwTA6+d0wdeOcbvltarl3jNwEtERETWxsBrx3JygH/+EZcffljeWvQHrm3dCpSUyFsLERERORYGXjumHy9bpw5Qu7a8tUREADVrirNG6HudiYiIiKyBgdeO6QNv/fry1gEATk5Az57icnKyvLUQERGRY2HgtWPnzonXDRrIW4cex/ESERGRHBh47Zg+8Cqhhxe4O443LU0cX0xERERkDQy8dkxpgTc0FGjSBCguBlJT5a6GiIiIHAUDrx1T0hhePQ5rICIiImtj4LVjShvDCzDwEhERkfUx8NoprRa4dElcVlIPb7dugEYDnDoFZGTIXQ0RERE5AgZeO3XxIqDTAS4ugJ+f3NXc5eMDdOggLnN6MiIiIrIGBl47pR/OEBwMqBX2U+awBiIiIrImhUUhshQljt/V0wfelBRxxgYiIiKi6sTAa6eUNiVZaTzNMBEREVkTA6+dUuKUZHoaDRAVJS5zWAMRERFVNwZeO6XkIQ3A3WENPHCNiIiIqhsDr51S8pAGgKcZJiIiIuth4LVDgqD8wBsSIp5muKQE2LZN7mqIiIjInjHw2qEbN4DcXHE5OFjeWirD6cmIiIjIGhh47ZC+d9fPD3B3l7eWyjDwEhERkTUw8NohpQ9n0OvaVTwpxunTwIULcldDRERE9oqB1w4peUqy0mrUAMLDxWWO4yUiIqLqwsBrh5Q+JVlp3buL1wy8REREVF0YeO2QrQxpABh4iYiIqPox8NohWwq8nTuLZ17LzBQvRERERJbGwGuHbGUMLwB4eQHt2onLqamylkJERER2ioHXzhQWApcvi8u2MIYX4LAGIiIiql4MvHbm4kXx2s0N8PWVtxapSgdeQZC3FiIiIrI/DLx2pvRwBpVK3lqk6tQJcHYGzp8H/vlH7mqIiIjI3jDw2hlbOmBNz8MDiIwUlzmsgYiIiCyNgdfO2NIcvKVxHC8RERFVFwZeO2OLPbzA3cCbmspxvERERGRZDLx2xpamJCutQwfA1RW4dAk4dUruaoiIiMieKCLwLl68GCEhIXBzc0NkZCT27dtX4bY//PADIiIiULNmTXh6eiIsLAxff/210TaCIGDatGkIDAyEu7s7oqKicMpBUpStDmlwcwMeeURc5rAGIiIisiTZA+/atWsRHx+PxMREHDx4EG3atEFMTAyuXLlicvvatWvjrbfeQlpaGo4cOYLY2FjExsZi8+bNhm3mzp2LDz/8EEuXLsXevXvh6emJmJgYFBQUWOtlyUIQbHdIA8BxvERERFQ9ZA+8CxYswNixYxEbG4vmzZtj6dKl8PDwwBdffGFy+27dumHQoEFo1qwZGjVqhAkTJqB169bYuXMnALF3d+HChXj77bcxYMAAtG7dGl999RUuXbqEDRs2WPGVWd+1a8CdO+LyAw/IW8v94DheIiIiqg5Ocj55UVERDhw4gISEBMM6tVqNqKgopKWl3fPxgiDgt99+w8mTJzFnzhwAQEZGBrKyshAVFWXYrkaNGoiMjERaWhqGDx9ebj+FhYUoLCw03M7JyQEAaLVaaLXa+359Uumfo6rPJc5h64yAAAFqdTGsULpFPfww4ObmhOxsFY4c0aJ58/LbWKqtHAXbSzq2lXRsK+nYVtKxraRjW4nMef2yBt5r166hpKQE/v7+Ruv9/f1x4sSJCh9369Yt1KtXD4WFhdBoNPjkk08QHR0NAMjKyjLso+w+9feVlZSUhBkzZpRbv2XLFnh4eJj1mqoiOTm5So/fsycQQHv4+NzAxo07LFOUlT34YEccOVIXn3xyHH37ZlS4XVXbytGwvaRjW0nHtpKObSUd20o6R2+r/Px8ydvKGnjvl7e3N9LT05Gbm4uUlBTEx8ejYcOG6Nat233tLyEhAfHx8YbbOTk5CA4ORq9eveDj42Ohqium1WqRnJyM6OhoODs73/d+zpwRR6i0alUTffv2tVR5VnX4sBpHjgDXrrVE377Nyt1vqbZyFGwv6dhW0rGtpGNbSce2ko5tJdJ/Iy+FrIHX19cXGo0G2dnZRuuzs7MREBBQ4ePUajUaN24MAAgLC8Px48eRlJSEbt26GR6XnZ2NwMBAo32GhYWZ3J+rqytcXV3LrXd2drbqG6mqz3fhgngdEqKGs7Psw7PvS1QUkJgI/P67GhqNGuoKXoa1fza2ju0lHdtKOraVdGwr6dhW0jl6W5nz2mVNRS4uLggPD0dKSophnU6nQ0pKCjp06CB5PzqdzjAGNzQ0FAEBAUb7zMnJwd69e83apy2y1SnJSmvXTjzV8LVrwF9/yV0NERER2QPZhzTEx8dj9OjRiIiIQPv27bFw4ULk5eUhNjYWADBq1CjUq1cPSUlJAMTxthEREWjUqBEKCwuxceNGfP3111iyZAkAQKVSYeLEiZg9ezaaNGmC0NBQTJ06FUFBQRg4cKBcL9MqbHlKMj1nZ6BzZ2DLFnF6slat5K6IiIiIbJ3sgXfYsGG4evUqpk2bhqysLISFhWHTpk2Gg87OnTsHdanvtfPy8jBu3DhcuHAB7u7uaNq0KVatWoVhw4YZtnnjjTeQl5eHF154ATdv3kTnzp2xadMmuLm5Wf31WZM9BF5AnJ5syxZxerJXX5W7GiIiIrJ1sgdeAIiLi0NcXJzJ+1JTU41uz549G7Nnz650fyqVCjNnzsTMmTMtVaLiFRQA+qHQth54u3YVr3//XZyPV6WStx4iIiKybbZ5ZBOVc/68eO3pCdSuLW8tVRUeLo7jvX4dOHZM7mqIiIjI1jHw2onSwxlsvUfUxQXQH1/4++/y1kJERES2j4HXTpw9K17b+nAGPf2whu3b5a2DiIiIbB8Dr52wlwPW9EoHXkGQtxYiIiKybQy8dsIe5uAtrX17wNUVyMoCTp+WuxoiIiKyZQy8dkIfeIOD5a3DUtzcgMhIcZnDGoiIiKgqGHjtxNWr4nUlZ2S2OY8+Kl4z8BIREVFVMPDaiWvXxGtfX3nrsKTS8/ESERER3S8GXjsgCHcDb5068tZiSR06AE5O4nCNzEy5qyEiIiJbxcBrB/LygKIicdmeeng9PYGICHGZwxqIiIjofjHw2gF9766bm3iGMnvCYQ1ERERUVQy8dqD0+F1bP8taWTwBBREREVUVA68duH5dvLan8bt6nToBajVw5gxw8aLc1RAREZEtYuC1A/Y4Q4Oejw/Qtq24zGENREREdD8YeO2APQdegMMaiIiIqGoYeO2APU5JVhpPQEFERERVwcBrB/RjeO21h7dLF/H6xAngyhV5ayEiIiLbw8BrB+x9SEPt2kCrVuLyjh12Ng0FERERVTsGXjtg70MagLvjeHfuZOAlIiIi8zDw2gF7H9IAlD4BBd+yREREZB6mBztg70MagLvjeI8eBW7fdpa3GCIiIrIpDLw2ThAcI/D6+wNNmwKCoMKxY3Y8doOIiIgsjoHXxuXmAkVF4rI9j+EF7k5PxsBLRERE5mDgtXH68btuboCHh7y1VDf9OF4GXiIiIjIHA6+NKz2cQWXnExjox/GeOVMDt2/LWwsRERHZDgZeG+cIU5LpBQcDoaECdDo10tLsPN0TERGRxTDw2jhHmJKstM6dBQA8AQURERFJx8Br4xxhhobSunTRAeAJKIiIiEg6Bl4b53iBV+zh3b9fhTt3ZC6GiIiIbAIDr43TD2lwhDG8ANCwIVC79h0UFamwd6/c1RAREZEtYOC1cY7Ww6tSAS1aiCn/999lLoaIiIhsAgOvjXO0wAsAzZsz8BIREZF0DLw2zpGmJdPT9/Du3n33LHNEREREFWHgtXGONi0ZAAQH34avr4A7d4ADB+SuhoiIiJSOgdeGCYJjDmlQqYBOncTZGjisgYiIiO6FgdeG5ebe/UrfkYY0AHenJ2PgJSIionth4LVh+uEMbm6Ah4e8tVjb3RNQACUlMhdDREREisbAa8NKD2dQOdiJx1q3Bnx8gJwc4MgRuashIiIiJWPgtWGOOH5XT6MBOncWl7dvl7cWIiIiUjYGXhvmaGdZK+vRR8VrjuMlIiKiyjDw2jBH7uEFjAOvIMhbCxERESkXA68Nc/TAGx4OuLuLPd3Hj8tdDRERESkVA68Nc8SzrJXm4gJ06CAuc1gDERERVYSB14Y54lnWyuraVbzmgWtERERUEQZeG+boQxqAu+N4t2/nOF4iIiIyjYHXhjHwApGR4tCGy5eBM2fkroaIiIiUSBGBd/HixQgJCYGbmxsiIyOxb9++Crddvnw5unTpglq1aqFWrVqIiooqt/2YMWOgUqmMLr17967ul2F1jj4tGSAetNa+vbjMYQ1ERERkiuyBd+3atYiPj0diYiIOHjyINm3aICYmBleuXDG5fWpqKkaMGIFt27YhLS0NwcHB6NWrFy5evGi0Xe/evXH58mXD5dtvv7XGy7EaQWAPr163buJ1aqqcVRAREZFSyR54FyxYgLFjxyI2NhbNmzfH0qVL4eHhgS+++MLk9t988w3GjRuHsLAwNG3aFJ999hl0Oh1SUlKMtnN1dUVAQIDhUqtWLWu8HKvJzQWKisRlRw+8pQ9c4zheIiIiKstJzicvKirCgQMHkJCQYFinVqsRFRWFtLQ0SfvIz8+HVqtF7dq1jdanpqbCz88PtWrVQo8ePTB79mzUqeC7/8LCQhQWFhpu5+TkAAC0Wi20Wq25L8ts+ucw57mysgDAGW5uApydi2GFMhXBVFtFRABOTk44f16FU6e0CA2VqzrluZ/3lqNiW0nHtpKObSUd20o6tpXInNevEgT5+sQuXbqEevXqYffu3eign1AVwBtvvIHt27dj796999zHuHHjsHnzZvz1119wc3MDAKxZswYeHh4IDQ3FmTNnMGXKFHh5eSEtLQ0ajabcPqZPn44ZM2aUW7969Wp4eHhU4RVWn9Ona+L117uiTp07+PzzLXKXI7vJk7vg5MnaeOWVQ+jZ85zc5RAREVE1y8/Px1NPPYVbt27Bx8en0m1l7eGtqvfeew9r1qxBamqqIewCwPDhww3LrVq1QuvWrdGoUSOkpqaiZ8+e5faTkJCA+Ph4w+2cnBzD2OB7NaAlaLVaJCcnIzo6Gs7OzpIes3mzCgDwwANu6Nu3b3WWpygVtdWuXWrMmwfcvNkGffu2lLFCZbmf95ajYltJx7aSjm0lHdtKOraVSP+NvBSyBl5fX19oNBpkZ2cbrc/OzkZAQEClj50/fz7ee+89bN26Fa1bt65024YNG8LX1xenT582GXhdXV3h6upabr2zs7NV30jmPN/Nm+K1r6/KId/sZduqZ09g3jxgxw41nJ1lH5quONZ+L9sytpV0bCvp2FbSsa2kc/S2Mue1y5oMXFxcEB4ebnTAmf4AtNJDHMqaO3cuZs2ahU2bNiEiIuKez3PhwgVcv34dgYGBFqlbCXiWNWMdOwIaDZCZCZw9K3c1REREpCSyd4XFx8dj+fLlWLlyJY4fP46XX34ZeXl5iI2NBQCMGjXK6KC2OXPmYOrUqfjiiy8QEhKCrKwsZGVlITc3FwCQm5uLSZMmYc+ePcjMzERKSgoGDBiAxo0bIyYmRpbXWB04JZkxb28gPFxc5ny8REREVJrsgXfYsGGYP38+pk2bhrCwMKSnp2PTpk3w9/cHAJw7dw6XL182bL9kyRIUFRXhySefRGBgoOEyf/58AIBGo8GRI0fQv39/PPjgg3juuecQHh6OHTt2mBy2YKsYeMsrPT0ZERERkZ4iDlqLi4tDXFycyftSy5xNIDMzs9J9ubu7Y/PmzRaqTLl4lrXyunUTx/Ey8BIREVFpsvfw0v1hD295nTsDajVw5gxw4YLc1RAREZFSMPDaKAbe8nx8gLZtxWX28hIREZEeA6+N0gdeDmkwxnG8REREVBYDrw0SBE5LVpFu3cRrBl4iIiLSY+C1Qbm5QFGRuMzAa6xLF0ClAv7+Gyg1uQcRERE5MAZeG6QfzuDuDnh4yFuL0tSsCbRpIy6zl5eIiIgABl6bxCnJKsdxvERERFQaA68N4gwNlWPgJSIiotIYeG0QA2/lHn1UvD5+HLhyRd5aiIiISH4MvDaIQxoqV6cO0KqVuMxeXiIiImLgtUHs4b03DmsgIiIiPQZeG8TAe2/6+Xi3bZO1DCIiIlIABl4bxMB7b/rAe+wYkJ0taylEREQkMwZeG8QxvPdWp87d+XjZy0tEROTYGHhtEHt4peneXbxm4CUiInJsDLw2iIFXmh49xGsGXiIiIsfGwGtjBIFDGqR69FFArQZOnQIuXJC7GiIiIpILA6+Nyc0FiorEZfbwVq5GDeDhh8Vl9vISERE5LgZeG6MfzuDuDnh4yFuLLeCwBiIiImLgtTEczmAe/YFrv/0mbx1EREQkHwZeG8MD1szTuTPg5AScPQtkZMhdDREREcmBgdfGMPCax8sLaN9eXGYvLxERkWNi4LUxHNJgPs7HS0RE5NgYeG3MrVvidc2aspZhU0ofuCYI8tZCRERE1sfAa2Nu3xavvb3lrcOWdOgAuLgAly4Bf/8tdzVERERkbQy8NiYnR7z28ZG3Dlvi7g507Cguc1gDERGR42HgtTH6wMseXvNwHC8REZHjYuC1MfohDezhNU/pwMtxvERERI6FgdfGcEjD/YmMFIc2XL0K/PWX3NUQERGRNTHw2hgOabg/Li7iSSgADmsgIiJyNAy8NoZDGu6ffnoynoCCiIjIsTDw2hj28N4//Tje7dsBnU7eWoiIiMh6GHhtDHt47194uPiPwo0bQHq63NUQERGRtTDw2pDCQvECMPDeDycn4NFHxWUOayAiInIcDLw2RN+7CwBeXvLVYcuiosTr5GR56yAiIiLrYeC1IfrA6+Eh9laS+aKjxesdO4CCAnlrISIiIutg4LUhPGCt6po3BwIDgTt3gN275a6GiIiIrIGB14bwgLWqU6nuDmvYulXeWoiIiMg6GHhtCM+yZhkMvERERI6FgdeGcEiDZfTsKV7/8Qfw77/y1kJERETVj4HXhnBIg2XUqyeO5RUEnmaYiIjIETDw2hAOabAcDmsgIiJyHAy8NkTfw8shDVWnn56M8/ESERHZPwZeG8IeXsvp2hXQaIAzZ4CMDLmrISIiourEwGtDeNCa5Xh7A488Ii5zWAMREZF9Y+C1ITxozbL0wxoYeImIiOybIgLv4sWLERISAjc3N0RGRmLfvn0Vbrt8+XJ06dIFtWrVQq1atRAVFVVue0EQMG3aNAQGBsLd3R1RUVE4depUdb+MaschDZalP3AtJQXQ6eSthYiIiKqP7IF37dq1iI+PR2JiIg4ePIg2bdogJiYGV65cMbl9amoqRowYgW3btiEtLQ3BwcHo1asXLl68aNhm7ty5+PDDD7F06VLs3bsXnp6eiImJQUFBgbVeVrXgkAbLat9ebMvr14H0dLmrISIiouoie+BdsGABxo4di9jYWDRv3hxLly6Fh4cHvvjiC5Pbf/PNNxg3bhzCwsLQtGlTfPbZZ9DpdEhJSQEg9u4uXLgQb7/9NgYMGIDWrVvjq6++wqVLl7BhwwYrvjLL45AGy3J2Brp1E5c5rIGIiMh+Ocn55EVFRThw4AASEhIM69RqNaKiopCWliZpH/n5+dBqtahduzYAICMjA1lZWYjSf18NoEaNGoiMjERaWhqGDx9ebh+FhYUoLCw03M75/65UrVYLrVZ7X6/NHPrnuNdz5eQ4AVDB3b0YWq1Q7XUpkdS2kqp7dzV++UWDLVt0eO21EovsU0ks3V72jG0lHdtKOraVdGwr6dhWInNev6yB99q1aygpKYG/v7/Ren9/f5w4cULSPiZPnoygoCBDwM3KyjLso+w+9feVlZSUhBkzZpRbv2XLFnh4eEiqwxKS7zEp7L//9gHggkOHtuPatVzrFKVQ92orqZydvQD0xO+/C/jxx01wdbXPwbyWai9HwLaSjm0lHdtKOraVdI7eVvn5+ZK3lTXwVtV7772HNWvWIDU1FW5ubve9n4SEBMTHxxtu5+TkGMYG+1hh/IBWq0VycjKio6Ph7OxschtBAO7cEX9cjz32KOrVq/ayFElKW5lDEICkJAGXLmlQo0Yf9OhhXz3nlm4ve8a2ko5tJR3bSjq2lXRsK5H+G3kpZA28vr6+0Gg0yM7ONlqfnZ2NgICASh87f/58vPfee9i6dStat25tWK9/XHZ2NgIDA432GRYWZnJfrq6ucHV1Lbfe2dnZqm+kyp7vzh2guFhcrl3bGQ78/gZg2Z9NdDSwciWwbZsTYmIsskvFsfZ72ZaxraRjW0nHtpKObSWdo7eVOa9d1oPWXFxcEB4ebjjgDIDhALQOHTpU+Li5c+di1qxZ2LRpEyIiIozuCw0NRUBAgNE+c3JysHfv3kr3qXT6A9YAwMtLvjrskX64Nw9cIyIisk+yD2mIj4/H6NGjERERgfbt22PhwoXIy8tDbGwsAGDUqFGoV68ekpKSAABz5szBtGnTsHr1aoSEhBjG5Xp5ecHLywsqlQoTJ07E7Nmz0aRJE4SGhmLq1KkICgrCwIED5XqZVabvtffyAtSyz61hX3r2FK8PHgSuXQN8feWth4iIiCxL9sA7bNgwXL16FdOmTUNWVhbCwsKwadMmw0Fn586dg7pUwluyZAmKiorw5JNPGu0nMTER06dPBwC88cYbyMvLwwsvvICbN2+ic+fO2LRpU5XG+cqNU5JVn8BAoE0b4PBhIDkZGDFC7oqIiIjIkmQPvAAQFxeHuLg4k/elpqYa3c7MzLzn/lQqFWbOnImZM2daoDpl4FnWqlfv3mLg/d//GHiJiIjsDb8ctxE8y1r16t1bvN68macZJiIisjf3FXi1Wi3Onz+PkydP4t9//7V0TWQChzRUr44dxfHRV67wNMNERET2RnLgvX37NpYsWYKuXbvCx8cHISEhaNasGerWrYsGDRpg7Nix2L9/f3XW6tDYw1u9XFzuHry2aZO8tRAREZFlSQq8CxYsQEhICL788ktERUVhw4YNSE9Px99//420tDQkJiaiuLgYvXr1Qu/evXHq1KnqrtvhsIe3+umHNTDwEhER2RdJB63t378fv//+O1q0aGHy/vbt2+PZZ5/F0qVL8eWXX2LHjh1o0qSJRQt1dDxorfrpTzqxezdw6xZQo4a89RAREZFlSAq83377raSdubq64qWXXqpSQWQahzRUv9BQ4KGHgJMngZQUYPBguSsiIiIiSzD7oLWrV69WeN+ff/5ZpWKoYhzSYB19+ojX//ufvHUQERGR5ZgdeFu1aoX//ve/5dbPnz8f7du3t0hRVB57eK2j9DheQZC3FiIiIrIMswNvfHw8nnjiCbz88su4c+cOLl68iJ49e2Lu3LlYvXp1ddRI4Bhea3n0UcDNDbhwATh2TO5qiIiIyBLMDrxvvPEG0tLSsGPHDrRu3RqtW7eGq6srjhw5gkGDBlVHjQQOabAWd3egWzdxmbM1EBER2Yf7OvFE48aN0bJlS2RmZiInJwfDhg1DQECApWujUjikwXo4PRkREZF9MTvw7tq1C61bt8apU6dw5MgRLFmyBK+88gqGDRuGGzduVEeNBPbwWpM+8P7+O5CXJ28tREREVHVmB94ePXpg2LBh2LNnD5o1a4bnn38ehw4dwrlz59CqVavqqJHAMbzW9OCDQEgIUFQEpKbKXQ0RERFVldmBd8uWLXjvvffg7OxsWNeoUSPs2rULL774okWLI5Eg3O3h5ZCG6qdS3e3l5fRkREREts/swNu1a1fTO1KrMXXq1CoXROXl5wM6nbjMHl7r0M/Hy3G8REREtk9S4F2zZo3kHZ4/fx67du2674KoPP1wBrUa8PCQtxZH0b074OwMnDkDnD4tdzVERERUFZIC75IlS9CsWTPMnTsXx48fL3f/rVu3sHHjRjz11FN4+OGHcf36dYsX6shKD2dQqeStxVF4ewOdO4vL7OUlIiKybZIC7/bt2zFnzhwkJyejZcuW8PHxQZMmTdCqVSs88MADqFOnDp599lnUr18fR48eRf/+/au7bofCA9bkoR/Hu3GjvHUQERFR1ThJ3bB///7o378/rl27hp07d+Ls2bO4c+cOfH190bZtW7Rt2xZq9X1N60v3wDl45dG3LzB5MvDbb+L0ZJ6ecldERERE90Ny4NX7z3/+g+eeew4DBw6shnLIFM7BK48WLcTpyTIzgZQUgF9cEBER2Sazu2Rv3bqFqKgoNGnSBO+++y4uXbpUHXVRKezhlYdKBTz+uLj8yy/y1kJERET3z+zAu2HDBly8eBEvv/wy1q5diwYNGqBPnz5Yv349tFptddTo8NjDKx994P3117tTwxEREZFtua9Bt3Xr1kV8fDwOHz6MvXv3onHjxnjmmWcQFBSE1157DadOnbJ0nQ6NB63J59FHAS8vICsLOHBA7mqIiIjoflTpKLPLly8jOTkZycnJ0Gg06Nu3L/788080b94cH3zwgaVqdHgc0iAfV1cgJkZc5rAGIiIi22R24NVqtfj+++/x2GOPoUGDBli3bh0mTpyIS5cuYeXKldi6dSu+++47zJw5szrqdUgc0iAvjuMlIiKybWbP0hAYGAidTocRI0Zg3759CAsLK7dN9+7dUbNmTQuURwB7eOXWt694AFt6OnD+PBAcLHdFREREZA6ze3g/+OADXLp0CYsXLzYZdgGgZs2ayMjIqGpt9P/YwyuvunWBDh3E5f/+V95aiIiIyHxmB95nnnkGbm5u1VELVYAHrcmPwxqIiIhsF0+NZgM4pEF++sCbkiKedY2IiIhsBwOvDeCQBvk1bw6EhgKFhcDWrXJXQ0REROZg4LUB7OGVn0oFPPaYuMxhDURERLaFgdcGcAyvMvCsa0RERLaJgVfhdDogN1dcZuCVV9euYi97djbwxx9yV0NERERSMfAqnD7sAhzSIDcXl7tnXfv1V3lrISIiIukYeBVOf8CakxPA2eDkx+nJiIiIbA8Dr8KVPmBNpZK3FhLPuqZW3z3rGhERESkfA6/C8YA1ZfH1vXvWNfbyEhER2QYGXoXjHLzKM3CgeP3DD7KWQURERBIx8Coc5+BVnsGDxevUVOD6dVlLISIiIgkYeBWOPbzK07AhEBYGlJQAP/0kdzVERER0Lwy8CsceXmV64gnxmsMaiIiIlI+BV+F40Joy6Yc1JCff/RkRERGRMjHwKhyHNChT8+ZA06ZAURFPQkFERKR0DLwKxyENysVhDURERLaBgVfh2MOrXPphDf/7H5CfL28tREREVDEGXoXjGF7latsWCAkRw+6mTXJXQ0RERBWRPfAuXrwYISEhcHNzQ2RkJPbt21fhtn/99ReeeOIJhISEQKVSYeHCheW2mT59OlQqldGladOm1fgKqheHNCiXSsVhDURERLZA1sC7du1axMfHIzExEQcPHkSbNm0QExODK1eumNw+Pz8fDRs2xHvvvYeAgIAK99uiRQtcvnzZcNm5c2d1vYRqxyENyqYf1vDLL0Bhoby1EBERkWmyBt4FCxZg7NixiI2NRfPmzbF06VJ4eHjgiy++MLl9u3btMG/ePAwfPhyurq4V7tfJyQkBAQGGi6+vb3W9hGrHHl5le+QRIChI/Dn99pvc1RAREZEpTnI9cVFREQ4cOICEhATDOrVajaioKKSlpVVp36dOnUJQUBDc3NzQoUMHJCUloX79+hVuX1hYiMJS3XM5/58ytVottFptlWqRQv8cpp4rJ8cJgAru7lpYoRTFq6yt5DJggBpLlmiwbp0OUVElcpdjRIntpVRsK+nYVtKxraRjW0nHthKZ8/plC7zXrl1DSUkJ/P39jdb7+/vjxIkT973fyMhIrFixAg899BAuX76MGTNmoEuXLjh69Ci8K+gmTUpKwowZM8qt37JlCzw8PO67FnMlJyeXW3fzZj8ATjh4MBUXL3IqAD1TbSWXwEBfAJ2wfr0Wjz22GRqNIHdJ5SipvZSObSUd20o6tpV0bCvpHL2t8s2YIkm2wFtd+vTpY1hu3bo1IiMj0aBBA3z33Xd47rnnTD4mISEB8fHxhts5OTkIDg5Gr1694GOFwbNarRbJycmIjo6Gs7OzYX1xMVBYKP6IHn+8G2x4ZIbFVNRWcurVC1i0SMD1667w9u6Lbt2UE3iV2F5KxbaSjm0lHdtKOraVdGwrUY4ZpzqVLfD6+vpCo9EgOzvbaH12dnalB6SZq2bNmnjwwQdx+vTpCrdxdXU1OSbY2dnZqm+kss+Xl3f3vtq1neHA7+lyrP2zqYyzMzBwIPD558BPPzkhOlruispTUnspHdtKOraVdGwr6dhW0jl6W5nz2mU7aM3FxQXh4eFISUkxrNPpdEhJSUGHDh0s9jy5ubk4c+YMAgMDLbZPa9H/4+LiAlRyjB4pgH62hh9+AHQ6eWshIiIiY7LO0hAfH4/ly5dj5cqVOH78OF5++WXk5eUhNjYWADBq1Cijg9qKioqQnp6O9PR0FBUV4eLFi0hPTzfqvX399dexfft2ZGZmYvfu3Rg0aBA0Gg1GjBhh9ddXVTzphO3o2ROoUQO4fBnYtUvuaoiIiKg0WcfwDhs2DFevXsW0adOQlZWFsLAwbNq0yXAg27lz56BW383kly5dQtu2bQ2358+fj/nz56Nr165ITU0FAFy4cAEjRozA9evXUbduXXTu3Bl79uxB3bp1rfraLIFz8NoOV1dg0CBgxQrg22+BLl3kroiIiIj0ZD9oLS4uDnFxcSbv04dYvZCQEAhC5QcErVmzxlKlyY5z8NqWESPEwLtuHbBoETjmmoiISCFkP7UwVYw9vLalRw/Azw+4dg3YulXuaoiIiEiPgVfB2MNrW5ycgKFDxeVvv5W3FiIiIrqLgVfBeNCa7dEfG/njj8CdO/LWQkRERCIGXgXjkAbb06ED0KABkJsL/Pe/cldDREREAAOvonFIg+1Rqe728q5eLW8tREREJGLgVTD28NomfeDduBG4dUveWoiIiIiBV9HYw2ubWrUCmjcHCgvFsbxEREQkLwZeBeNBa7ap9LAGztZAREQkPwZeBeOQBtulD7xbtwLZ2fLWQkRE5OgYeBWMQxpsV6NGQPv2gE4nnnmNiIiI5MPAq2Ac0mDbOKyBiIhIGRh4FUw/pIE9vLZp6FBxPO/u3UBmptzVEBEROS4GXgVjD69tCwoCuncXl9eskbcWIiIiR8bAq1BFReK0VgADry3TD2v45htAEOSthYiIyFEx8CqUfjgDwCENtuzJJwE3N+DoUeDgQbmrISIickwMvAqlH87g5gY4OclbC92/mjWBQYPE5S+/lLUUIiIih8XAq1D5+eK1l5e8dVDVjRkjXq9eDRQUyFoKERGRQ2LgVSh94PXwkLcOqrqePYEHHgBu3AB+/lnuaoiIiBwPA69CMfDaD40GGD1aXOawBiIiIutj4FWoO3fEa3d3eesgy9APa9iyBbh4UdZSiIiIHA4Dr0Kxh9e+NG4MdOkinmr466/lroaIiMixMPAqFAOv/dH38n75JefkJSIisiYGXoVi4LU/Q4aIP8+//wbS0uSuhoiIyHEw8CoUA6/98fYWQy/Ag9eIiIisiYFXoXjQmn2KjRWv164F8vLkrYWIiMhRMPAqFHt47VOXLkDDhuKpo3/8Ue5qiIiIHAMDr0Ix8NontZpz8hIREVkbA69CMfDar9GjAZUK+O03IDNT7mqIiIjsHwOvQukDL8fw2p8GDYAePcRl9vISERFVPwZehdIftMYeXvv0/PPi9fLlgFYrby1ERET2joFXoTikwb4NHgz4+QGXLwM//yx3NURERPaNgVehGHjtm4vL3V7eTz6RtxYiIiJ7x8CrUAy89u+FF8RZG377DThxQu5qiIiI7BcDr0LxoDX716AB0K+fuLx0qby1EBER2TMGXoXiQWuOYdw48XrFCp55jYiIqLow8CoUhzQ4hl69xDOv3boFrFkjdzVERET2iYFXoRh4HYNaDbz0kri8ZIm8tRAREdkrBl6FYuB1HLGxgKsrcOAAsH+/3NUQERHZHwZeBSopAYqKxGUetGb/fH2BIUPEZU5RRkREZHkMvAqkP2ANYA+vo9AfvLZmDfDvv/LWQkREZG8YeBVIP5wBANzc5KuDrOeRR4A2bYCCAnHGBiIiIrIcBl4FKj0Hr5o/IYegUt3t5V26FNDp5K2HiIjInjBOKRBPOuGYnnoK8PEBTp0CNm+WuxoiIiL7wcCrQDzphGPy8gKee05cfv99eWshIiKyJwy8CsQpyRzXhAmARgOkpADp6XJXQ0REZB8YeBWIgddxNWhwd4oy9vISERFZhuyBd/HixQgJCYGbmxsiIyOxb9++Crf966+/8MQTTyAkJAQqlQoLFy6s8j6ViIHXsf3nP+L1mjXAhQvy1kJERGQPZA28a9euRXx8PBITE3Hw4EG0adMGMTExuHLlisnt8/Pz0bBhQ7z33nsICAiwyD6ViAetObaICKBrV6C4GPjoI7mrISIisn2yBt4FCxZg7NixiI2NRfPmzbF06VJ4eHjgiy++MLl9u3btMG/ePAwfPhyurq4W2acS8aA10vfyfvopcPu2vLUQERHZOie5nrioqAgHDhxAQkKCYZ1arUZUVBTS0tKsus/CwkIUFhYabufk5AAAtFottFrtfdViDv1z6K9v31YD0MDNTQettqTan9+WlG0re9WrF/Dgg074+28Vli0rwauv3t/EvI7SXpbAtpKObSUd20o6tpV0bCuROa9ftsB77do1lJSUwN/f32i9v78/Tpw4YdV9JiUlYcaMGeXWb9myBR5W7GZNTk4GABw61ARAc/z773ls3Jhutee3Jfq2smc9ezbA33+HYc6cQoSGboVGI9z3vhyhvSyFbSUd20o6tpV0bCvpHL2t8kufmvYeZAu8SpKQkID4+HjD7ZycHAQHB6NXr17w8fGp9ufXarVITk5GdHQ0nJ2dsW+fONLkwQcfQN++QdX+/LakbFvZs+7dgfXrBVy96oE7d/pi6FDzA68jtVdVsa2kY1tJx7aSjm0lHdtKpP9GXgrZAq+vry80Gg2ys7ON1mdnZ1d4QFp17dPV1dXkmGBnZ2ervpH0z1dUJN729NTA2Vljtee3Jdb+2cjB2RkYPx6YPh1YtMgJTz0lnoL4/vZl/+1lKWwr6dhW0rGtpGNbSefobWXOa5ftoDUXFxeEh4cjJSXFsE6n0yElJQUdOnRQzD7lwGnJSG/cOMDNDdi/H9ixQ+5qiIiIbJOsszTEx8dj+fLlWLlyJY4fP46XX34ZeXl5iI2NBQCMGjXK6AC0oqIipKenIz09HUVFRbh48SLS09Nx+vRpyfu0BQy8pFe3LjB6tLg8f768tRAREdkqWcfwDhs2DFevXsW0adOQlZWFsLAwbNq0yXDQ2blz56BW383kly5dQtu2bQ2358+fj/nz56Nr165ITU2VtE9bwMBLpcXHA8uWAb/8Ahw+DLRpI3dFREREtkX2g9bi4uIQFxdn8j59iNULCQmBINz7wJ3K9mkLGHiptAcfBIYNE8+8NnMm8P33cldERERkW2Q/tTCVpz/xBM+0RnpTp4oHrP3wA3DkiNzVEBER2RYGXgViDy+V1bw5MGSIuDxrlry1EBER2RoGXgVi4CVTpk4Vr9evB44elbcWIiIiW8LAq0AMvGRKy5bAk0+Ky+zlJSIiko6BV4H0gZdjeKmsadPE63XrgGPH5K2FiIjIVjDwKpD+oDX28FJZrVoBgwcDgsBeXiIiIqkYeBWIQxqoMvpe3rVrgePH5a2FiIjIFjDwKoxOBxQUiMsMvGRKmzbAwIFiL+/s2XJXQ0REpHwMvAqjH84AMPBSxfS9vGvWACdPylsLERGR0jHwKkzpwMuD1qgibdsC/fuL3wgkJspdDRERkbIx8CqMfvyuqyug5k+HKjFzpnj2tbVrgf375a6GiIhIuRipFIYHrJFUbdoAzzwjLk+aJI7pJSIiovIYeBWGgZfMMWuW+G3A9u3Axo1yV0NERKRMDLwKw8BL5qhfH5gwQVx+4w2guFjeeoiIiJSIgVdh9Aet8YA1kiohAahdWzzz2sqVcldDRESkPAy8CsMeXjJXzZrA22+Ly9OmAXl5spZDRESkOAy8CsPAS/dj3DggNBS4dAlYuFDuaoiIiJSFgVdhGHjpfri6Au++Ky7PmQNcuSJvPURERErCwKsw+sDLMbxkrqFDgYgI4PZtcfYGIiIiEjHwKoz+oDX28JK51Gpg7lxxeelSnnKYiIhIj4FXYTikgaqie3fgscfE6cleeYUnoyAiIgIYeBWHgZeqauFCcUxvcjLw/fcqucshIiKSHQOvwjDwUlU1agS8+aa4PGmSBnfuaOQtiIiISGYMvArDg9bIEiZPBho2BC5eVGHt2ofkLoeIiEhWDLwKw4PWyBLc3YEPPxSXf/mlEf76S956iIiI5MTAqzAc0kCW0q8f8PjjOpSUqDFxooYHsBERkcNi4FUYBl6ypPffL4GLSzG2b1fj22/lroaIiEgeDLwKw8BLlhQSAgwZcgoA8J//ALduyVsPERGRHBh4FUY/hpcHrZGlDBx4Gk2aCMjKAhIT5a6GiIjI+hh4FYY9vGRpzs46LFxYAgD46CNgzx6ZCyIiIrIyBl6FYeCl6hAdLeDppwGdDoiNBQoK5K6IiIjIehh4FYaBl6rLokVAQABw4gQwbZrc1RAREVkPA6/CMPBSdaldG1i2TFx+/30ObSAiIsfBwKsggsCD1qh6Pf448Mwz4tCGMWPuvt+IiIjsGQOvgpQeV8keXqouixYBgYHAyZMc2kBERI6BgVdB9MMZAPbwUvWpVct4aENamrz1EBERVTcGXgXRB14XF8DJSd5ayL499hgwapQ4jIZDG4iIyN4x8CqIPvCyd5esYeFCICgI+PtvICFB7mqIiIiqDwOvguh72Th+l6yhVi1g+XJxedEi4Oef5a2HiIioujDwKsidOyoADLxkPX37Aq+9Ji6PGQOcOydrOURERNWCgVdBOAcvyeG994CICODGDWDECECrlbsiIiIiy2LgVRAGXpKDiwuwdi3g4wPs3g0kJspdERERkWUx8CoITzpBcmnYEPjsM3E5KQnYvFneeoiIiCyJgVdBeNAayWnIEODll8XlZ54BLl+Wtx4iIiJLYeBVkPx8HrRG8lqwAGjdGrh6FRg5EigpkbsiIiKiqmPgVRCO4SW5ubkB330HeHoC27YBU6bIXREREVHVMfAqCAMvKcFDD90dzzt3LvD11/LWQ0REVFWKCLyLFy9GSEgI3NzcEBkZiX379lW6/bp169C0aVO4ubmhVatW2Lhxo9H9Y8aMgUqlMrr07t27Ol+CRfCgNVKK4cPv9u6OHQvs2SNvPURERFUhe+Bdu3Yt4uPjkZiYiIMHD6JNmzaIiYnBlStXTG6/e/dujBgxAs899xwOHTqEgQMHYuDAgTh69KjRdr1798bly5cNl2+//dYaL6dKeNAaKcmsWcCAAUBhITBwIHDhgtwVERER3R/ZA++CBQswduxYxMbGonnz5li6dCk8PDzwxRdfmNx+0aJF6N27NyZNmoRmzZph1qxZePjhh/Hxxx8bbefq6oqAgADDpVatWtZ4OVXCg9ZISdRqcThDq1ZAdrYYfvXDboiIiGyJk5xPXlRUhAMHDiAhIcGwTq1WIyoqCmlpaSYfk5aWhvj4eKN1MTEx2LBhg9G61NRU+Pn5oVatWujRowdmz56NOnXqmNxnYWEhCgsLDbdzcnIAAFqtFlornHZK/xy5uToAari6lkCr1VX789oifVtZ4+diD6raXm5uwPffAx07OuHgQRVGj9bhm29KoFJZskpl4HtLOraVdGwr6dhW0rGtROa8flkD77Vr11BSUgJ/f3+j9f7+/jhx4oTJx2RlZZncPisry3C7d+/eGDx4MEJDQ3HmzBlMmTIFffr0QVpaGjQaTbl9JiUlYcaMGeXWb9myBR5W7G49e/YqgECcOfMnNm48a7XntUXJyclyl2BTqtper71WB4mJHbF+vRrOzicxbNjfFqpMefjeko5tJR3bSjq2lXSO3lb5ZnztKGvgrS7Dhw83LLdq1QqtW7dGo0aNkJqaip49e5bbPiEhwajXOCcnB8HBwejVqxd8fHyqvV6tVovk5GR4e/sBANq1a4m+fVtU+/PaIn1bRUdHw9nZWe5yFM9S7dW3L1Cnjg4vvaTGt982Q/fuTTBmjGDBSuXH95Z0bCvp2FbSsa2kY1uJ9N/ISyFr4PX19YVGo0F2drbR+uzsbAQEBJh8TEBAgFnbA0DDhg3h6+uL06dPmwy8rq6ucHV1Lbfe2dnZqm+kggLxe2IfHyc48PtXEmv/bGydJdrrxReBf/4Rpyp76SUn1K0rHsxmb/jeko5tJR3bSjq2lXSO3lbmvHZZD1pzcXFBeHg4UlJSDOt0Oh1SUlLQoUMHk4/p0KGD0faA2KVf0fYAcOHCBVy/fh2BgYGWKbya8KA1Urr33gOeew7Q6YBhw8STUxARESmd7LM0xMfHY/ny5Vi5ciWOHz+Ol19+GXl5eYiNjQUAjBo1yuigtgkTJmDTpk14//33ceLECUyfPh1//PEH4uLiAAC5ubmYNGkS9uzZg8zMTKSkpGDAgAFo3LgxYmJiZHmNUvHEE6R0KhWwdCkwaBBQVAT07w/88YfcVREREVVO9jG8w4YNw9WrVzFt2jRkZWUhLCwMmzZtMhyYdu7cOajVd3N5x44dsXr1arz99tuYMmUKmjRpgg0bNqBly5YAAI1GgyNHjmDlypW4efMmgoKC0KtXL8yaNcvksAUlKSgQr3niCVIyJydg9WqgXz/gt9+APn2AnTvFM7QREREpkeyBFwDi4uIMPbRlpaamlls3ZMgQDBkyxOT27u7u2Lx5syXLsxr28JKtcHMDNmwAevQQe3ijo4Fdu4DgYLkrIyIiKk/2IQ10FwMv2RJvb2DjRrFn9/x5MfyePy93VUREROUx8CqEIDDwku2pWxfYsgUIDQVOnwYefRTIyJC7KiIiImMMvAqh1aohCJylgWxP/frA9u1AkyZAZqYYek+dkrsqIiKiuxh4FaKo6O4Z4HjQGtma4GAx9DZrBly4IIbeY8fkroqIiEjEwKsQhYVi4HVyAk86QTYpMBBITQVatQKysoBu3YAjR+SuioiIiIFXMfSBl8MZyJb5+Ykno3j4YeDqVaB7d2DvXrmrIiIiR8fAqxAMvGQv6tQBUlKAyEjg33/F0Pvjj3JXRUREjoyBVyEYeMme1KwJbN0K9O0L3LkDPPEEsHCh3FUREZGjYuBVCP1BazxgjeyFlxfw00/ASy+J0+699howYQJQUiJ3ZURE5GgYeBWCPbxkj5ycgE8+AebOFW9/+CEweDCQlydvXURE5FgYeBWCgZfslUoFTJoEfPcd4OoK/Pwz0LUrcO6c3JUREZGjYOBVCAZesndDhgC//SYe1HbggDiTQ3Ky3FUREZEjYOBVCH3g5RhesmcdOwL794th9/p1ICYGeOcdQKeTuzIiIrJnDLwKoT9ojT28ZO9CQ4Fdu4DnnxcPZnv7bWDAAODGDbkrIyIie8XAqxAc0kCOxM0NWL4c+PxzcVzvr78C4eHAwYNyV0ZERPaIgVch2MNLjujZZ4Hdu4GQECAjA3jkESApiVOXERGRZTHwKgR7eMlRPfyweBDbwIGAVgtMmQI8+ihw5ozclRERkb1g4FUIHrRGjqx2beCHH4AvvwS8vcVe3zZtxGEPgiB3dUREZOsYeBWCQxrI0alUwJgxwJEjYg9vXh7wwgtA//7ApUtyV0dERLaMgVchOKSBSBQSAmzbBsyfD7i4iAe0NW0qnqWtuFju6oiIyBYx8CoEAy/RXWo18J//iGN7IyOB27eBCROA9u2Bffvkro6IiGwNA69CMPASldeypTied+lSoGZN4NAhcSaHceOAmzflro6IiGwFA69C6Mfw8qA1ImNqNfDii8CJE8Azz4gHsS1ZAjz4oHit1cpdIRERKR0Dr0Kwh5eocv7+wFdfAb/9Jo7pvXpV7Olt2RL48UfO5kBERBVj4FUIBl4iabp3Bw4fBj76CKhbF/j7b2DwYKBzZ3H4AxERUVkMvArBwEsknYsLEBcHnD4NvP22OBRo926gUydgwADgjz/krpCIiJSEgVchCgudADDwEpnDxweYNQs4dQp4/nlxvO/PPwPt2gF9+rDHl4iIRAy8CiAIQFGR+KPgQWtE5qtXTzwr219/AaNGARoNsGmT2OPbo4c47pdjfImIHBcDrwJotYBOJ/4o2MNLdP+aNgVWrgROngTGjgWcncWTWPTsCUREiPcVFMhdJRERWRsDrwLk599dZuAlqrpGjYBly4AzZ4BXXgHc3ICDB8VTF9evD0ybxtMVExE5EgZeBdAHXo1GgLOzvLUQ2ZPgYPGUxOfPA0lJwAMPiNOZzZoFNGgAjBghDnfQ6eSulIiIqhMDrwLcuSNeu7sDKpW8tRDZI19f4M03gYwMYN06oEsXoLgYWLNGHO7QqBEwa5YaV65wED0RkT1i4FUAfQ8vhzMQVS8nJ+DJJ4HffxeHOLz0kjjTQ2YmMGuWBi++GI0+fTRYtQrIyZG7WiIishQGXgW4c0fs1mXgJbKetm3FUxNfvgysWgX06KGDIKiQkqLGM88Afn7AoEFiL3BurtzVEhFRVTDwKoC+h5dTkhFZn4cHMHIksGlTCT79NBlvv12Chx4CCguBDRvEcb5+fsCQIcDq1cCNG3JXTERE5mLgVYC7Qxo4USiRnPz98zFtmg7Hj4unL54yRRzfe+cOsH69GIzr1gW6dQPmzxenPyMiIuVj4FWA0getEZH8VCqgdWvgnXfEs7gdOCAe9NaiBVBSAmzfDkyaJM7726QJMH488MMP7P0lIlIqJ7kLIB60RqRkKhXw8MPiJSlJnOnh11/Fy7ZtwOnT4uWTT8RTGz/8MBAVJZ7h7ZFHAG9vuV8BEREx8CqA/qA19vASKV9oqHgyi1deAW7fFufxTUkBtm4Fjh8H/vhDvLz3nhiAw8KAzp3FS6dOQFCQ3K+AiMjxMPAqAHt4iWyTtzcwYIB4AYCLF++G3x07xOnODh4ULx9+KG4THAy0a3f3Eh4O1Kwp1ysgInIMDLwKwMBLZB/q1QNGjRIvAHDhArBrF7Bzp3h9+LB41rfz58Uxv3pNmog9wa1bA23aiJfgYJ6IhojIUhh4FeDuQWucpYHInjzwADBsmHgBxCEQBw8C+/ffvWRkiAfGnTolngVOr2ZNoGVLoFmzu5fmzRmEiYjuBwOvAnCWBiLH4O0NdO0qXvSuXxdD8OHDdy/HjwM3b4o9wzt3Gu/D01PsEW7c+O61/hIQII4bJiIiYwy8CsAhDUSOq04dIDpavOgVFYmh9+hR4MQJcfn4cbEXOC8PSE8XL2W5uAANGgAhIXcvDRqIPc0PPCAOuXBzs8rLIiJSFAZeBcjP56mFieguF5e7Y3lL02qBf/4Rg69+OjT9cmamGJT1wyMqUqeOGH6DgoDAQLFXODDw7rK/v3hyDR8fDp0gIvvBwKsAHNJARFI4OwMPPSReytJqxVkiMjPFy9mzd68vXhQPlLtzRxxCcf26OHSiMi4uYvD18xOv69S5e6lZU41z5+pBo1Ghbl2gVi3xUrOmWCMRkdIoIvAuXrwY8+bNQ1ZWFtq0aYOPPvoI7du3r3D7devWYerUqcjMzESTJk0wZ84c9O3b13C/IAhITEzE8uXLcfPmTXTq1AlLlixBkyZNrPFyzKYPvDy1MBHdL2fnu8MYTBEEcVzwhQti+L18GcjKMr6+fBm4ehXIzRV7iy9eFC/laQBE4IMPyt/j5QXUqCH2EJe99vYuf/HyEscle3oaL3t6ip0AGo2lWoiIHJnsgXft2rWIj4/H0qVLERkZiYULFyImJgYnT56En59fue13796NESNGICkpCY899hhWr16NgQMH4uDBg2jZsiUAYO7cufjwww+xcuVKhIaGYurUqYiJicGxY8fgpsABbPoxvOzhJaLqolLd7Ylt1arybe/cEYPvlSvi5erVuz3D168DV6/qcOrUdajVvrh5U4UbN4CcHPGxubnixXRQNp+Lizjcy8ND/B2pv7i5GS/rL66uxssuLuJ16WUXl7sXZ2fjZVMXJ6e71/plHhxIZFtkD7wLFizA2LFjERsbCwBYunQp/vvf/+KLL77Am2++WW77RYsWoXfv3pg0aRIAYNasWUhOTsbHH3+MpUuXQhAELFy4EG+//TYG/P9s8F999RX8/f2xYcMGDB8+3HovTiIetEZESuLuDtSvL15M0WpLsHHjbvTt2xfO/z+GobgYuHULhvB769bdi/52bq44NVvpS26ueCCe/pKbe/d3IiD2NBcVib3TSqJS3Q3ATk5iT3TZZY0G0GiccOdOD9So4VRqnRiY9ctlb6vVd2/rlyu7qFQV39Yvl74ufSm7ztQ2+ov+dZt7f9n1+ttlr3U6NY4eDcHFi2poNOW3MXfZ3MeV/fmau62U9eaOi69oH8XFKhw6FIT8fBWc7jPJWWKMvql9uLsDpb50VwxZA29RUREOHDiAhIQEwzq1Wo2oqCikpaWZfExaWhri4+ON1sXExGDDhg0AgIyMDGRlZSEqKspwf40aNRAZGYm0tDSTgbewsBCFhYWG2zn/31Wh1Wqh1Wrv+/VJlZcnfmfn4lIMrZbDGiqj/3lY4+diD9he0rGtpKuorXx8xEtV6XRAQYHY05yff/dy547KsP7OHXEb8bYKhYVAYaF4++61CkVFMNyn1YrXRUXiclGRyhCotdqKL4JQ/q+6INy9v3IqAN64cKHq7WL/NADa3HMrAsT41k7uIkx64AEB//xTbJXnMuf3tayB99q1aygpKYG/v7/Ren9/f5w4ccLkY7Kyskxun5WVZbhfv66ibcpKSkrCjBkzyq3fsmULPKzQ7ern9zB0Ok+cOnUYWm1OtT+fPUhOTpa7BJvC9pKObSWdXG2lUt0d5mANOh1QUqJGSYkKxcUqlJSoodOpUFIiXnQ6dallleG+0temLoKggk4HE+thuF+/rF9fdp1YX/n77q6/e59OJ74e/Tr9NhWvM15f2bJ+ez39Y03dFsr065TeV+l1prc1vr+se91vatuy25d9zsr3UXkd0vZR9eerTubUBwA+PkXYuHF/9RRTRn7pr4PuQfYhDUqQkJBg1Guck5OD4OBg9OrVCz6W6K64h+hoLZKTkxEdHW34epBM02rZVuZge0nHtpKObSUd20o6tpV0ym8r64xp0H8jL4WsgdfX1xcajQbZ2dlG67OzsxEQEGDyMQEBAZVur7/Ozs5GYGCg0TZhYWEm9+nq6gpXV9dy652dna36RrL289kytpV52F7Ssa2kY1tJx7aSjm0lnaO3lTmvXdbjTF1cXBAeHo6UlBTDOp1Oh5SUFHTo0MHkYzp06GC0PSB+rabfPjQ0FAEBAUbb5OTkYO/evRXuk4iIiIjsl+xDGuLj4zF69GhERESgffv2WLhwIfLy8gyzNowaNQr16tVDUlISAGDChAno2rUr3n//ffTr1w9r1qzBH3/8gWXLlgEAVCoVJk6ciNmzZ6NJkyaGacmCgoIwcOBAuV4mEREREclE9sA7bNgwXL16FdOmTUNWVhbCwsKwadMmw0Fn586dg7rUhIcdO3bE6tWr8fbbb2PKlClo0qQJNmzYYJiDFwDeeOMN5OXl4YUXXsDNmzfRuXNnbNq0SZFz8BIRERFR9ZI98AJAXFwc4uLiTN6Xmppabt2QIUMwZMiQCvenUqkwc+ZMzJw501IlEhEREZGN4rliiIiIiMiuMfASERERkV1j4CUiIiIiu8bAS0RERER2jYGXiIiIiOwaAy8RERER2TUGXiIiIiKyawy8RERERGTXGHiJiIiIyK4x8BIRERGRXWPgJSIiIiK7xsBLRERERHaNgZeIiIiI7JqT3AUokSAIAICcnByrPJ9Wq0V+fj5ycnLg7Oxslee0VWwr87C9pGNbSce2ko5tJR3bSjq2lUif0/S5rTIMvCbcvn0bABAcHCxzJURERERUmdu3b6NGjRqVbqMSpMRiB6PT6XDp0iV4e3tDpVJV+/Pl5OQgODgY58+fh4+PT7U/ny1jW5mH7SUd20o6tpV0bCvp2FbSsa1EgiDg9u3bCAoKglpd+Shd9vCaoFar8cADD1j9eX18fBz6jWsOtpV52F7Ssa2kY1tJx7aSjm0lHdsK9+zZ1eNBa0RERERk1xh4iYiIiMiuMfAqgKurKxITE+Hq6ip3KYrHtjIP20s6tpV0bCvp2FbSsa2kY1uZjwetEREREZFdYw8vEREREdk1Bl4iIiIismsMvERERERk1xh4iYiIiMiuMfAqwOLFixESEgI3NzdERkZi3759cpekOElJSWjXrh28vb3h5+eHgQMH4uTJk3KXZRPee+89qFQqTJw4Ue5SFOnixYt4+umnUadOHbi7u6NVq1b4448/5C5LcUpKSjB16lSEhobC3d0djRo1wqxZsySdw94R/P7773j88ccRFBQElUqFDRs2GN0vCAKmTZuGwMBAuLu7IyoqCqdOnZKnWJlV1lZarRaTJ09Gq1at4OnpiaCgIIwaNQqXLl2Sr2AZ3et9VdpLL70ElUqFhQsXWq0+W8LAK7O1a9ciPj4eiYmJOHjwINq0aYOYmBhcuXJF7tIUZfv27Rg/fjz27NmD5ORkaLVa9OrVC3l5eXKXpmj79+/Hp59+itatW8tdiiLduHEDnTp1grOzM/73v//h2LFjeP/991GrVi25S1OcOXPmYMmSJfj4449x/PhxzJkzB3PnzsVHH30kd2mKkJeXhzZt2mDx4sUm7587dy4+/PBDLF26FHv37oWnpydiYmJQUFBg5UrlV1lb5efn4+DBg5g6dSoOHjyIH374ASdPnkT//v1lqFR+93pf6f3444/Ys2cPgoKCrFSZDRJIVu3btxfGjx9vuF1SUiIEBQUJSUlJMlalfFeuXBEACNu3b5e7FMW6ffu20KRJEyE5OVno2rWrMGHCBLlLUpzJkycLnTt3lrsMm9CvXz/h2WefNVo3ePBgYeTIkTJVpFwAhB9//NFwW6fTCQEBAcK8efMM627evCm4uroK3377rQwVKkfZtjJl3759AgDh7Nmz1ilKoSpqqwsXLgj16tUTjh49KjRo0ED44IMPrF6bLWAPr4yKiopw4MABREVFGdap1WpERUUhLS1NxsqU79atWwCA2rVry1yJco0fPx79+vUzen+RsZ9//hkREREYMmQI/Pz80LZtWyxfvlzushSpY8eOSElJwd9//w0AOHz4MHbu3Ik+ffrIXJnyZWRkICsry+izWKNGDURGRvJ3vQS3bt2CSqVCzZo15S5FcXQ6HZ555hlMmjQJLVq0kLscRXOSuwBHdu3aNZSUlMDf399ovb+/P06cOCFTVcqn0+kwceJEdOrUCS1btpS7HEVas2YNDh48iP3798tdiqL9888/WLJkCeLj4zFlyhTs378fr776KlxcXDB69Gi5y1OUN998Ezk5OWjatCk0Gg1KSkrwzjvvYOTIkXKXpnhZWVkAYPJ3vf4+Mq2goACTJ0/GiBEj4OPjI3c5ijNnzhw4OTnh1VdflbsUxWPgJZszfvx4HD16FDt37pS7FEU6f/48JkyYgOTkZLi5ucldjqLpdDpERETg3XffBQC0bdsWR48exdKlSxl4y/juu+/wzTffYPXq1WjRogXS09MxceJEBAUFsa2oWmi1WgwdOhSCIGDJkiVyl6M4Bw4cwKJFi3Dw4EGoVCq5y1E8DmmQka+vLzQaDbKzs43WZ2dnIyAgQKaqlC0uLg6//vortm3bhgceeEDuchTpwIEDuHLlCh5++GE4OTnByckJ27dvx4cffggnJyeUlJTIXaJiBAYGonnz5kbrmjVrhnPnzslUkXJNmjQJb775JoYPH45WrVrhmWeewWuvvYakpCS5S1M8/e9z/q6XTh92z549i+TkZPbumrBjxw5cuXIF9evXN/yuP3v2LP7zn/8gJCRE7vIUh4FXRi4uLggPD0dKSophnU6nQ0pKCjp06CBjZcojCALi4uLw448/4rfffkNoaKjcJSlWz5498eeffyI9Pd1wiYiIwMiRI5Geng6NRiN3iYrRqVOnctPb/f3332jQoIFMFSlXfn4+1GrjPxkajQY6nU6mimxHaGgoAgICjH7X5+TkYO/evfxdb4I+7J46dQpbt25FnTp15C5JkZ555hkcOXLE6Hd9UFAQJk2ahM2bN8tdnuJwSIPM4uPjMXr0aERERKB9+/ZYuHAh8vLyEBsbK3dpijJ+/HisXr0aP/30E7y9vQ3j3mrUqAF3d3eZq1MWb2/vcmObPT09UadOHY55LuO1115Dx44d8e6772Lo0KHYt28fli1bhmXLlsldmuI8/vjjeOedd1C/fn20aNEChw4dwoIFC/Dss8/KXZoi5Obm4vTp04bbGRkZSE9PR+3atVG/fn1MnDgRs2fPRpMmTRAaGoqpU6ciKCgIAwcOlK9omVTWVoGBgXjyySdx8OBB/PrrrygpKTH8vq9duzZcXFzkKlsW93pflf1nwNnZGQEBAXjooYesXaryyT1NBAnCRx99JNSvX19wcXER2rdvL+zZs0fukhQHgMnLl19+KXdpNoHTklXsl19+EVq2bCm4uroKTZs2FZYtWyZ3SYqUk5MjTJgwQahfv77g5uYmNGzYUHjrrbeEwsJCuUtThG3btpn8HTV69GhBEMSpyaZOnSr4+/sLrq6uQs+ePYWTJ0/KW7RMKmurjIyMCn/fb9u2Te7Sre5e76uyOC1ZxVSCwNPkEBEREZH94hheIiIiIrJrDLxEREREZNcYeImIiIjIrjHwEhEREZFdY+AlIiIiIrvGwEtEREREdo2Bl4iIiIjsGgMvEREREdk1Bl4iIiIismsMvERERERk1xh4iYiIiMiuMfASEdmpq1evIiAgAO+++65h3e7du+Hi4oKUlBQZKyMisi6VIAiC3EUQEVH12LhxIwYOHIjdu3fjoYceQlhYGAYMGIAFCxbIXRoRkdUw8BIR2bnx48dj69atiIiIwJ9//on9+/fD1dVV7rKIiKyGgZeIyM7duXMHLVu2xPnz53HgwAG0atVK7pKIiKyKY3iJiOzcmTNncOnSJeh0OmRmZspdDhGR1bGHl4jIjhUVFaF9+/YICwvDQw89hIULF+LPP/+En5+f3KUREVkNAy8RkR2bNGkS1q9fj8OHD8PLywtdu3ZFjRo18Ouvv8pdGhGR1XBIAxGRnUpNTcXChQvx9ddfw8fHB2q1Gl9//TV27NiBJUuWyF0eEZHVsIeXiIiIiOwae3iJiIiIyK4x8BIRERGRXWPgJSIiIiK7xsBLRERERHaNgZeIiIiI7BoDLxERERHZNQZeIiIiIrJrDLxEREREZNcYeImIiIjIrjHwEhEREZFdY+AlIiIiIrv2f6gm1S7Bn9okAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Решение линейного уравнения 2-ого порядка\n",
    "#с начальными условиями y(0)=0 и y′(0)=1. Мы решим это уравнение и построим график решения.\n",
    "\n",
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Определяем дифференциальное уравнение второго порядка\n",
    "def ode(x, y):\n",
    "    dydx = np.zeros_like(y)\n",
    "    dydx[0] = y[1]\n",
    "    dydx[1] = -2 * y[1] - y[0]\n",
    "    return dydx\n",
    "\n",
    "# Начальные условия\n",
    "x0 = 0.0  # Начальная точка\n",
    "y0 = [0.0, 1.0]  # Начальные значения y(0) и y'(0)\n",
    "\n",
    "# Интервал интеграции\n",
    "x_span = (0.0, 15.0)  # От 0 до 5\n",
    "\n",
    "# Решение дифференциального уравнения\n",
    "sol = solve_ivp(ode, x_span, y0, t_eval=np.linspace(x_span[0], x_span[1], 100))\n",
    "\n",
    "# Извлечение результатов\n",
    "x_values = sol.t\n",
    "y_values = sol.y[0]\n",
    "\n",
    "# Построение графика решения\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_values, y_values, label='Решение', color='blue')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y(x)')\n",
    "plt.title('Решение линейного дифференциального уравнения 2-го порядка')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Функция, представляющая систему дифференциальных уравнений равноускоренного движения\n",
    "def acceleration(t, y):\n",
    "    x, v = y\n",
    "    dxdt = v\n",
    "    dvdt = a\n",
    "    return [dxdt, dvdt]\n",
    "\n",
    "# Начальные условия\n",
    "x0 = 0.0  # Начальная позиция\n",
    "v0 = 10.0  # Начальная скорость\n",
    "a = 5.0  # Ускорение\n",
    "\n",
    "# Временные точки для решения\n",
    "t_span = (0.0, 5.0)  # Временной интервал от 0 до 5 секунд\n",
    "\n",
    "# Решение уравнения\n",
    "sol = solve_ivp(acceleration, t_span, [x0, v0], t_eval=np.linspace(0, 5, 500))\n",
    "\n",
    "# Извлечение результатов\n",
    "t = sol.t\n",
    "x = sol.y[0]\n",
    "v = sol.y[1]\n",
    "\n",
    "# Построение графика позиции от времени\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(t, x, label='Позиция (x(t))', color='blue')\n",
    "plt.xlabel('Время (сек)')\n",
    "plt.ylabel('Позиция (м)')\n",
    "plt.title('Решение дифференциального уравнения равноускоренного движения')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Решение краевой задачи для ОДУ\n",
    "Для решения задачи с граничными условиями вы можете использовать библиотеку scipy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Пример и отображение краевой задачи для ОДУ\n",
    "# В этом примере мы определяем ОДУ справа ode, задаем краевые условия boundary_conditions, задаем интервал интеграции, начальное приближение и решаем краевую задачу с помощью solve_bvp из scipy. Затем мы строим график решения, полученного для функции y(x).\n",
    "# Обратите внимание, что в этом примере рассматривается краевая задача для уравнения y'' + sin(y) = 0 с краевыми условиями y(0) = π/4 и y(1) = 3π/4. Вы можете изменить ОДУ и краевые условия в соответствии с вашей конкретной задачей.\n",
    "\n",
    "import numpy as np\n",
    "from scipy.integrate import solve_bvp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Определение правой части ОДУ\n",
    "def ode(x, y):\n",
    "    dydx = np.vstack((y[1], -np.sin(y[0])))\n",
    "    return dydx\n",
    "\n",
    "# Определение краевых условий\n",
    "def boundary_conditions(ya, yb):\n",
    "    return np.array([ya[0] - np.pi/4, yb[0] - 3*np.pi/4])\n",
    "\n",
    "# Задание начальной и конечной точки для интеграции\n",
    "x_values = np.linspace(0, 1, 100)  # Интервал интеграции от 0 до 1\n",
    "\n",
    "# Задание начального приближения для решения\n",
    "initial_guess = np.zeros((2, x_values.size))\n",
    "\n",
    "# Решение краевой задачи\n",
    "solution = solve_bvp(ode, boundary_conditions, x_values, initial_guess)\n",
    "\n",
    "# Получение решения\n",
    "x_solution = solution.x\n",
    "y_solution = solution.y[0]\n",
    "\n",
    "# Строим график решения\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_solution, y_solution, label='Solution', color='blue')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y(x)')\n",
    "plt.title('Решение краевой задачи для ОДУ')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
